cp's OEIS Frontend

A381808 Number of multisets that can be obtained by choosing a strict integer partition of m for each m = 0..n and taking the multiset union.

%I A381808 #8 Jun 04 2025 21:09:03
%S A381808 1,1,1,2,4,12,38,145,586,2619,12096,58370,285244,1436815,7281062,
%T A381808 37489525,193417612
%N A381808 Number of multisets that can be obtained by choosing a strict integer partition of m for each m = 0..n and taking the multiset union.
%e A381808 The a(1) = 1 through a(5) = 12 multisets:
%e A381808   {1}  {1,2}  {1,2,3}    {1,2,3,4}      {1,2,3,4,5}
%e A381808               {1,1,2,2}  {1,1,2,2,4}    {1,1,2,2,4,5}
%e A381808                          {1,1,2,3,3}    {1,1,2,3,3,5}
%e A381808                          {1,1,1,2,2,3}  {1,1,2,3,4,4}
%e A381808                                         {1,2,2,3,3,4}
%e A381808                                         {1,1,1,2,2,3,5}
%e A381808                                         {1,1,1,2,2,4,4}
%e A381808                                         {1,1,1,2,3,3,4}
%e A381808                                         {1,1,2,2,2,3,4}
%e A381808                                         {1,1,2,2,3,3,3}
%e A381808                                         {1,1,1,1,2,2,3,4}
%e A381808                                         {1,1,1,2,2,2,3,3}
%t A381808 Table[Length[Union[Sort/@Join@@@Tuples[Select[IntegerPartitions[#],UnsameQ@@#&]&/@Range[n]]]],{n,0,10}]
%Y A381808 Set systems: A050342, A116539, A296120, A318361.
%Y A381808 The number of possible choices was A152827, non-strict A058694.
%Y A381808 Set multipartitions with distinct sums: A279785, A381718.
%Y A381808 Choosing prime factors: A355746, A355537, A327486, A355744, A355742, A355741.
%Y A381808 Choosing divisors: A355747, A355733.
%Y A381808 Constant instead of strict partitions: A381807, A066843.
%Y A381808 A000041 counts integer partitions, strict A000009, constant A000005.
%Y A381808 A066723 counts partitions coarser than {1..n}, primorial case of A317141.
%Y A381808 A265947 counts refinement-ordered pairs of integer partitions.
%Y A381808 A321470 counts partitions finer than {1..n}, primorial case of A300383.
%Y A381808 Cf. A001970, A018818, A213385, A299200, A321467, A321468, A321471, A321514, A355731, A381453, A381455.
%K A381808 nonn,more
%O A381808 0,4
%A A381808 _Gus Wiseman_, Mar 14 2025
%E A381808 a(12)-a(16) from _Christian Sievers_, Jun 04 2025